Healthcare cyber-physical system significantly facilitates healthcare services and patient treatment effectiveness by analyzing patients’ health information data conveniently. Nevertheless, it also develops the threats to the confidentiality of health information, patients’ privacy, and decidability of medical disputes. And, with the advances of quantum computing technology, most existing anonymous authentication schemes are becoming a growing threat to traditional cryptosystems. To address these problems, for healthcare cyber-physical systems, we propose a new lattice-based self-enhancement authorized accessible privacy authentication scheme by using a strong designated verifier double-authentication-preventing signature technique, called SEAPA. The SEAPA achieves three security and privacy requirements including unforgeability, anonymity for patients’ information, and self-enhancement for patients themselves. A detailed security proof shows our proposal achieves those required security goals. Finally, our construction is demonstrated by parameter analysis and performance evaluation to have reasonable efficiency.